Question

Numbers 50, 42, \[2x + 10\], \[2x - 8\], 12, 11, 8, 6 are written in descending order and their median is 25. Find \[x\]?
A.20
B.25
C.12
D.11

Answer 1

Hint: First we will use formula to calculate the median value by first calculating \[\dfrac{{n + 1}}{2}\], where \[n\] is the number of values in a set of data. Then we will use the formula to calculate the median by adding these middle values of the given set and then divide it by 2.

Complete step-by-step answer:
We are given that the numbers are 50, 42, \[2x + 10\], \[2x - 8\], 12, 11, 8, 6, which are in descending order.
We are also given that the median is 25.
We know the formula to find the median value by first calculating \[\dfrac{{n + 1}}{2}\], where \[n\] is the number of values in a set of data.
After finding the number of observations, we have that \[n = 9\].
Substituting the value of \[n\] in the above formula, we get
\[
   \Rightarrow \dfrac{{9 + 1}}{2} \\
   \Rightarrow \dfrac{{10}}{2} \\
   \Rightarrow 5 \\
 \]
So, we will take the 5th terms from the terms in descending orders, we have \[2x - 8\].
We know the formula to calculate the median by adding these middle values of the given set and then divide it by 2.
So, taking the 5th term equals to 25, we get
\[ \Rightarrow 25 = 2x - 8\]
Adding the above equation by 8 on both sides, we get
\[
   \Rightarrow 25 + 8 = 2x - 8 + 8 \\
   \Rightarrow 33 = 2x \\
 \]
Dividing the above equation by 2 on both sides, we get
\[
   \Rightarrow \dfrac{{33}}{2} = \dfrac{{2x}}{2} \\
   \Rightarrow 16.5 = x \\
   \Rightarrow x = 16.5 \\
 \]

Therefore, the required value is \[16.5\].

Note: We need to know that the mean is adding the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count. Do not forget any marks by adding up the values. We need to know if the value from \[\dfrac{{n + 1}}{2}\], where \[n\] is the number of values in a set of data is an integer than there is only one median value or else there will be two values.